In an arithmetic sequence, you start from the first element, and then you generate the next one by adding a common difference.
So, let's say you start from [tex] x [/tex] and add a common difference of [tex] d [/tex]. The first elements are
[tex] a_1=x[/tex]
[tex] a_2=x+d[/tex]
[tex] a_3=(x+d)+d=x+2d [/tex]
[tex] a_4=(x+2d)+d=x+3d [/tex]
[tex] a_5=(x+3d)+d=x+4d [/tex]
Since we know that [tex] a_5 = 53 [/tex], and [tex] x = -3 [/tex], we can solve for [tex]d [/tex]:
[tex] a_5 = x+4d \iff 53 = -3+4d \iff 56 = 4d \iff d = \dfrac{56}{4} = 14 [/tex]
So, the common difference is 14
